Modems are typically utilized for transmitting and receiving digital data communication from computer systems. Typically, data is expressed in a binary form. Data is transmitted at a bit rate, e.g., B bits per second, where the bit rate is defined as the number of bits to be transmitted and received, including the actual binary information data rate and a predetermined redundancy needed by coding in a selected system. During transmission, the binary data information is typically transmitted and received in a form of a series of symbols at a symbol rate of S symbols per second. Thus, each symbol contains B/S bits of binary data.
Each symbol can be represented by one of the possible line signal states generated by the modem. Various modulation techniques may be used to convert data into line signal states. For example, in quadrature amplitude modulation (QAM), The line signal states can be represented by a set of complex numbers, namely by a set of points in a two-dimensional signal constellation. For example, for a bit rate B and a symbol rate S, where B/S is an integer D, a signal constellation of size 2.sup.D is needed to represent D bits in each symbol. Thus, if B=12000 bits/second and the symbol rate S is 2400 symbols/second, D=5 bits/symbol, and a 32-point two-dimensional signal constellation is used, providing a scheme for mapping one out of 32 possible complex signal points according to 5 input data bits.
However, for high speed modems, multiple symbol rates and bit rates may be used to facilitate more efficient use of the available channel bandwidth. In such instances, the ratio B/S may not be always an integer.
Where B/S is not an integer, the modem transmits a fractional number of bits per symbol. Various techniques have been used to accomplish transmission of a fractional number of bits per symbol. In the constellation switching technique, for example, where D-1&lt;B/S&lt;D, the modem switches between D-1 bits/symbol and D bits/symbol such that, on an average, the modem sends B/S bits per symbol. Namely, the modem switches between a signal constellation with 2.sup.D-1 points and another signal constellation with 2.sup.D points.
The main disadvantages of constellation switching are the introduction of a variation in constellation size and an increase in peak-to-average power ratio due to the increase in constellation size. This is undesirable in many applications, especially when the communication channel introduces signal-dependent impairments such as harmonic distortion and pulse coded modulation (PCM) noise. In addition, constellation switching often complicates the modem implementation.
In contrast to one symbol by one symbol mapping techniques, frame-mapping techniques may be used.
Since B/S is usually a rational number, there exists a number N such that Q=N*B/S is an integer, i.e., the number of bits in a frame of N symbols is an integer. A frame-mapping algorithm maps the incoming Q bits to N symbols chosen from a signal constellation with a sufficiently large number of points. Compared with the constellation required by symbol-based constelation switching (with 2.sup.D points), frame-mapping techniques usually require a relatively small constellation, and thus a small peak-to-average power ratio. However, such techniques generally introduce complexity where a large N is used. Examples of frame-mapping techniques include modulus conversion and shell mapping.
Since multiple B and S values are often selected, there is often difficulty in selecting a reasonably small N such that Q=N*B/S is always an integer for all possible combinations of B and S. In some instances, a different N may be selected for different combinations of B and S, thereby further complicating the implementation of the mapping algorithm. Another approach is to transmit a fractional number of bits per frame, i.e., using a fixed N in conjunction with a constellation switching among frames. Both approaches provide more implementation complexity.
Hence, there is a need for a frame-mapping device and method which maps data that is transmitted at fractional bits per frame rate such that the implementation difficulties of constellation switching are avoided.